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Solving high-order uncertain differential equations via Adams–Simpson method

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Abstract

High-order uncertain differential equations are used to model differentiable uncertain systems with high-order differentials. Since most of high-order differential equations have no analytic solutions, how to design numerical methods for solving the high-order uncertain differential equation has always been a core issue in practice. This paper designs a numerical method for solving high-order uncertain differential equations via Adams–Simpson method. A procedure is designed, and some numerical experiments are given to illustrate the efficiency and effectiveness of the Adams–Simpson method. Furthermore, this paper gives how to calculate the expected value, the inverse uncertainty distributions of the extreme value, and the integral of the solution of the high-order uncertain differential equation with the aid of Adams–Simpson method.

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Acknowledgements

This research is funded by the Natural Science Foundation of Xinjiang (Grant No. 2020D01C017), National Natural Science Foundation of China (Grants Nos. 12061072, 11861064), and National Natural Science Foundation of China—Joint Key Program of Xinjiang (Grant No. U1703262).

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Authors and Affiliations

  1. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, China

    Yudong Hou, Lijun Wu & Yuhong Sheng

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  1. Yudong Hou
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  2. Lijun Wu
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  3. Yuhong Sheng
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Correspondence to Lijun Wu or Yuhong Sheng.

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Communicated by Valeria Neves Domingos Cavalcanti.

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Hou, Y., Wu, L. & Sheng, Y. Solving high-order uncertain differential equations via Adams–Simpson method. Comp. Appl. Math. 40, 252 (2021). https://doi.org/10.1007/s40314-020-01408-z

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  • DOI: https://doi.org/10.1007/s40314-020-01408-z

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